The intersection of complemented submodules is not complemented

Koen van den Dungen; Bram Mesland; Adam Rennie

doi:10.1016/j.jmaa.2023.127002

paper

The intersection of complemented submodules is not complemented

arXiv:2302.04631 · doi:10.1016/j.jmaa.2023.127002

Abstract

We show by (counter)example that the intersection of complemented submodules in a Hilbert $C^{*}$ -module is not necessarily complemented, answering an open question from [MR].

Addendum to : The Friedrichs angle and alternating projections in Hilbert $C^{*}$ -modules, J. Math. Anal. Appl. 516 (1) (2022) 126474, arXiv:2112.03822